Renormalization of quark propagators from twisted-mass lattice QCD at N{sub f}=2

Journal Article · Fri Apr 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.074506· OSTI ID:21537732

Blossier, B; Boucaud, Ph; Pene, O; Petrov, K ^[1]; Brinet, M ^[2]; De Soto, F ^[3]; Liu, Z ^[4]; Morenas, V ^[5]; Rodriguez-Quintero, J ^[6]

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1. Laboratoire de Physique Theorique, CNRS, and Universite Paris-Sud XI, Batiment 210, 91405 Orsay Cedex (France)
2. Laboratoire de Physique Subatomique et de Cosmologie, CNRS/IN2P3/UJF, 53 avenue des Martyrs, 38026 Grenoble (France)
3. Departamento Sistemas Fisicos, Quimicos y Naturales, Universidad Pablo de Olavide, 41013 Sevilla (Spain)
4. DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
5. Laboratoire de Physique Corpusculaire, Universite Blaise Pascal, CNRS/IN2P3, 63177 Aubiere Cedex (France)
6. Departamento Fisica Aplicada, Facultad Ciencias Experimentales, Universidad de Huelva, 21071 Huelva (Spain)

We present results concerning the nonperturbative evaluation of the renormalization constant for the quark field, Z{sub q}, from lattice simulations with twisted-mass quarks and three values of the lattice spacing. We use the regularization-invariant momentum-subtraction (RI'-MOM) scheme. Z{sub q} has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalization constants. We recall and develop the nonperturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice-spacing artefacts indeed scale as a{sup 2}p{sup 2}. We then study the running of Z{sub q} with particular attention to the nonperturbative effects, presumably dominated by the dimension-two gluon condensate <A{sup 2}> in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units, confirming that it is a continuum effect. It gives a {approx}4% contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally, combining all our results and using the known Wilson coefficient of <A{sup 2}>, we find g{sup 2}({mu}{sup 2})<A{sup 2}>{sub {mu}}{sup 2}{sub CM}=2.01(11)({sub -0.73}{sup +0.61})GeV{sup 2} at {mu}=10 GeV, the local operator A{sup 2} being renormalized in the MS scheme. This last result is in fair agreement within uncertainties with the value independently extracted from the strong coupling constant. We convert the nonperturbative part of Z{sub q} from the regularization-invariant momentum-subtraction (RI'-MOM) scheme to MS. Our result for the quark field renormalization constant in the MS scheme is Z{sub q} {sup MS} {sup pert}((2 GeV){sup 2},g{sub bare}{sup 2})=0.750(3)(7)-0.313(20)(g{sub bare}{sup 2}-1.5) for the perturbative contribution and Z{sub q}{sup MSnonperturbative}((2 GeV){sup 2},g{sub bare}{sup 2})=0.781(6)(21)-0.313(20)(g{sub bare}{sup 2}-1.5) when the nonperturbative contribution is included.

• OSTI ID: 21537732
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 7; Other Information: DOI: 10.1103/PhysRevD.83.074506; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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